Bernhard Banaschewski - Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L۸۵ ۴K۱, Canada.
Anthony W. Hager - Department of Mathematics and CS, Wesleyan University, Middletown, CT ۰۶۴۵۹.

 The category of the title is called \mathcal{W}. This has all free objects F(I) (I a set). For an object class \mathcal{A}, H\mathcal{A} consists of all homomorphic images of \mathcal{A}-objects. This note continues the study of the H-closed monoreflections (\mathcal{R}, r) (meaning H\mathcal{R} = \mathcal{R}), about which we show ({\em inter alia}): A \in \mathcal{A} if and  only if A is a countably up-directed union from H\{rF(\omega)\}. The meaning of this is then analyzed for two important cases: the maximum essential monoreflection r = c^{۳}, where c^{۳}F(\omega) = C(\RR^{\omega}), and C \in H\{c(\RR^{\omega})\} means C = C(T), for T a closed subspace of \RR^{\omega}; the epicomplete, and maximum, monoreflection, r = \beta, where \beta F(\omega) = B(\RR^{\omega}), the Baire functions, and E \in H\{B(\RR^{\omega})\} means E is {\em an} epicompletion (not ``the'') of such a C(T).

Archimedean ell-group, H-closed monoreflection, Yosida representation, countable composition, epicomplete, Baire functions